|
%I #4 Apr 04 2015 08:35:10
%S 0,1,2,4,7,12,20,33,72,196,710,1546,2599,6738,19553,80688,185625,
%T 978142,2432840,12112678,29466988,39202128,40962878,41948928,42570288,
%U 42684103,43265540,44518036,52194742,65214030,159581828,337649208
%N Partial sums of Iccanobif numbers A001129.
%C The only primes in this sequence are: 2, 7 and 19553. The squares in this sequence begin: 0, 1, 4, 196.
%F a(n) = SUM[i=0..n] A001129(i) = SUM[i=0..n] {a(0) = 0, a(1) = 1, a(i+2) = R(a(i)) + R(a(i+1))} = SUM[i=0..n] A001129(i) = SUM[i=1..n] {a(0) = 0, a(1) = 1, a(i+2) = A004086(a(i)) + A004086(a(i+1))}.
%e a(14) = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 39 + 124 + 514 + 836 + 1053 + 4139 + 12815 = 19553 is prime. a(31) = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 39 + 124 + 514 + 836 + 1053 + 4139 + 12815 + 61135 + 104937 + 792517 + 1454698 + 9679838 + 17354310 + 9735140 + 1760750 + 986050 + 621360 + 113815 + 581437 + 1252496 + 7676706 + 13019288 + 94367798 + 178067380.
%t nxt[{a_,b_}]:={b,Total[FromDigits/@Reverse/@IntegerDigits[{a,b}]]};Accumulate[ Transpose[NestList[nxt,{0,1},40]][[1]]] (* _Harvey P. Dale_, Apr 04 2015 *)
%Y Cf. A000040, A000045, A001129, A004086, A014258-A014260.
%K base,easy,nonn
%O 0,3
%A _Jonathan Vos Post_, Feb 06 2010
|
